// Source : https://leetcode-cn.com/problems/increasing-decreasing-string/
// Author : jkbs487
// Date   : 2020-12-16

/***************************************************************************************************** 
 *
 * Given a string s. You should re-order the string using the following algorithm:
 * 
 * 	Pick the smallest character from s and append it to the result.
 * 	Pick the smallest character from s which is greater than the last appended character to the 
 * result and append it.
 * 	Repeat step 2 until you cannot pick more characters.
 * 	Pick the largest character from s and append it to the result.
 * 	Pick the largest character from s which is smaller than the last appended character to the 
 * result and append it.
 * 	Repeat step 5 until you cannot pick more characters.
 * 	Repeat the steps from 1 to 6 until you pick all characters from s.
 * 
 * In each step, If the smallest or the largest character appears more than once you can choose any 
 * occurrence and append it to the result.
 * 
 * Return the result string after sorting s with this algorithm.
 * 
 * Example 1:
 * 
 * Input: s = "aaaabbbbcccc"
 * Output: "abccbaabccba"
 * Explanation: After steps 1, 2 and 3 of the first iteration, result = "abc"
 * After steps 4, 5 and 6 of the first iteration, result = "abccba"
 * First iteration is done. Now s = "aabbcc" and we go back to step 1
 * After steps 1, 2 and 3 of the second iteration, result = "abccbaabc"
 * After steps 4, 5 and 6 of the second iteration, result = "abccbaabccba"
 * 
 * Example 2:
 * 
 * Input: s = "rat"
 * Output: "art"
 * Explanation: The word "rat" becomes "art" after re-ordering it with the mentioned algorithm.
 * 
 * Example 3:
 * 
 * Input: s = "leetcode"
 * Output: "cdelotee"
 * 
 * Example 4:
 * 
 * Input: s = "ggggggg"
 * Output: "ggggggg"
 * 
 * Example 5:
 * 
 * Input: s = "spo"
 * Output: "ops"
 * 
 * Constraints:
 * 
 * 	1 <= s.length <= 500
 * 	s contains only lower-case English letters.
 ******************************************************************************************************/

class Solution {
public:
    string sortString(string s) {
        string ans;
        map<char, int> pool;
        for(char c : s) pool[c]++;
        while(ans.size() < s.size()) {
            for(auto it = pool.begin(); it != pool.end(); it++) {
                if(it->second > 0) ans += it->first;
                it->second--;
            }
            for(auto it = pool.rbegin(); it != pool.rend(); it++) {
                if(it->second > 0) ans += it->first;
                it->second--;
            }
        }
        return ans;
    }
};
